For Which derivative rule is used first? How do you know?
For Which derivative rule is used first? How do you know? d (4x3 - 3x714 dx...
In the previous question we used the chain rule to calculate the derivative fog indirectly from the derivatives off and g. Of course, in the previous question f and g were polynomials, and so a simpler method to find the derivative would be to first evaluate f g and then differentiate. However, this "simpler" method does not always work. For example, use the chain rule f(8(x)) = f'(8(x))g'(x) to evaluate: di sin(x3 +1) = d e(x3+1) -1) = datan-1(x3 +...
Calculate the first AND second derivative dy/dx and d^2y/dx^2 for the curve given by: r(t) = t-t, y(t) = 3t - t
The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate f(x) dx, where f is the function whose graph is shown below. The estimates were 0.7811 0.8675, 0.8632, and 0.9540, and the same number of subintervals were used in each case. (a) Which rule produced which estimate? ?1. Trapezoidal Rule estimate 2. Right-hand estimate 3. Left-hand estimate N4. Midpoint Rule estimate (b) Between which two approximations does the true value of o fa) dx lie? A. 0.8675 β...
Please answer all or do not answer. Thank you :) The Chain Rule and Directional Derivative: (a) Calculate by the chain rule given F(x,y) = x2 + y’, x = eu+20, y=uv. ov Use the chain rule (chain rule required!) to evaluate the partial derivative. OG where G(x,y) = x2 - y2 ,x=e"cosv, y = e"sinv. ди (c) Find the directional derivative in the direction of v=<12,-5> at (2,2) for f(x, y) = exy_y? and also the directional derivative in...
How do you do this problem? 3. Let h be a function whose first derivative is h/(x) = S:* 3(In( + 3))? dt. For 6 < x < 12, which of the following is true? Oh is increasing and the graph of his concave down. Oh is increasing and the graph of h is concave up. Oh is decreasing and the graph of h is concave down. 0 h is decreasing and the graph of h is concave up. Oh...
. Find the first derivatives (dy/dx) for each of the following functions. Do not need to simplify. (3 points each) A. y = (2x^5 + 3x^3)^2 B. y = (8x^3-56x^2+3x)/(x+12) C. y= (6x2 + 3x) (x – 4x3)
Below are eight functions. Find the first derivative of each. Space is provided. Use good dark ink if you are returning this by a scanned version. All of the derivatives can be found by using combinations of the constant rule, power function rule and sum-difference rule. Do not use the product rule. It is not needed. The degree of difficulty (more or less) increases from (a-h). Be sure to show intermediate work. Check the scoring rubric to see how the points are awarded. For example, the first...
I know the first derivative gives you the critical point which is the harmonic mean but I’m having trouble proving it because my calculus is a little subpar. I also need help proving why there is a minimum at that critical point using the second derivative. Thanks! are portive at the vale of 邝 the harmonte mean
Question 1 (1 point) Determine the following definite integral 2 4x3 + 28x5 + 36 dx x2 1 Question 2 (1 point) A particle has velocity function given by v(t) = 64-192. Determine the total distance traveled over the interval [0.7]. Do not include units in your answer. Question 3 (1 point) Suppose g(3) = 5 and g'(3) = 26. Determine the derivative F'(3), where r9(30) F(x) = La Red 4 1 + t2 dt.
✓ 4. Derive an order h2 accurate one-sided finite difference approximation to the first derivative dø/dx at the point x = tj. Suppose that the numerical solution di is available at the set of points {C;} and assume constant grid spacing, i.e. h = i+1 - Ti is the same for all i. The derivative must be calculated using ; and only points to its left (i.e. Xj, 2j-1, *;-2, ... use as many as you need). Hint: assume that...